I would have some concerns about using whiten strips with your retainer. Keep in mind what whiten strips are. Whiting strips are like bleach for your teeth this may not be good for the metal part of your retainer.
I would suggest even though it may be more costly that you have your teeth whiten by your dentist. They would be able to make sure you do not damage your retainer in the process. At the very least call your dentist and see what they have to say about using the whiting strips product before using it.